After hearing many people talk about how great Izotope Ozone is, I decided to invest in it. The other day I noticed when I applied it to only one channel of a stereo pair of audio tracks, it causes a slight delay. I also sometimes use it on the master bus. I'm wondering if using a couple of instances of Izotope and also maybe some other plug-ins could cause enough delay to cause lip sync errors?

I had some problems with this. I did some reading and some fiddling, but it was so many years ago I'm forgetting the exact adjustments I did... this is what I learned in the process:

Yes, plugins such as Ozone do produce delays. All that computation that's going on is significant enough that an affected track does take some time getting out of the box during preview. This effect is usually known as "Latency."

One thing you don't mention - is this on preview only, or does it render this way? Pretty important to know this, you'll want to test this if you haven't yet done so. These plugin latency effects shouldn't be audible in a render.

Addressing preview latency has been difficult for me, but my understanding is as follows:
a) Many plugins and even Vegas can produce some latency in audio playback. In extreme cases, this will sound like little breaks and discontinuities in the playback.

b) Sound cards have adjustable buffers to counteract this problem. The basic idea is to adjust buffer size upwards to the smallest possible amount to eliminate playback problems. This is a system-wide control.

c) You want the minimum buffer size that you can get away with, because i) you're increasing the delay of playback for all sources, and ii) if you do any multitrack recording against playback this plays hob with sync.

d) There are other places that audio buffer size can be adjusted that are more specific to what you may be experiencing.

There are also buffer size controls in Vegas. Options | Audio Device | Playback Buffering, and Track Buffering. Even more if you click on the "advanced" button on that dialog.

I did some adjustments in all these places to optimize playback and sync. But this was a couple systems ago, and my more recent systems with higher performance processors and better sound cards haven't had these problems.